1. Chapter 2: Modeling Distributions of Data
2.1: Describing Location in a Distribution
-Find & Interpret the Percentile of an individual value within a distribution of data.
-Estimate Percentiles and individual values using a cumulative relative frequency graph.
-Find and Interpret the standardized score (z-score) of an individual value within a distribution of data.

2. Percentile:
The pth Percentile of a distribution is the value with p percent of the observations less than it.

3. Some books say Less than or equal to….
Percentile:
The pth Percentile of a distribution is the value with p percent of the observations less than it.
Some books say Less than or equal to….

4. Some books say Less than or equal to….
Percentile:
The pth Percentile of a distribution is the value with p percent of the observations less than it.
Some books say Less than or equal to….
Finding Percentiles:

5. Some books say Less than or equal to….
Percentile:
The pth Percentile of a distribution is the value with p percent of the observations less than it.
Some books say Less than or equal to….
Finding Percentiles:
1)List smallest to biggest

6. Some books say Less than or equal to….
Percentile:
The pth Percentile of a distribution is the value with p percent of the observations less than it.
Some books say Less than or equal to….
Finding Percentiles:
1)List smallest to biggest
2) count the observations below targeted #

7. Frequency:

8. Frequency: The amount of observations

9. Frequency: how often the observations occur in a certain
Relative Frequency: the percentage of frequency, Divide the count of each by the total x 100

10. Frequency: how often the observations occur in a certain
Relative Frequency: the percentage of frequency, Divide the count of each by the total x 100
Cumulative Frequency: Add the counts from the frequency column for the current class and all the classes with smaller values of the variable

11. Frequency: how often the observations occur in a certain
Relative Frequency: the percentage of frequency, Divide the count of each by the total x 100
Cumulative Frequency: Add the counts from the frequency column for the current class and all the classes with smaller values of the variable
Cumulative Relative Frequency: Divide the entries in the cumulative frequency column by the total # of individuals x 100

12. Cumulative Relative Frequency Graph

13. Cumulative Relative Frequency Graph

14. Cumulative Relative Frequency Graph
Chapter 1 test scores

15. Check Your Understanding
Mark receives a score report detailing her performance on the statewide test. On the math section, Mark earned a raw score fo 39, which placed him at the 68th Percentile. That means that
a)Mark did better than about 39% of the students who took the test.
b) Mark did worse than about 39% of the students who took the test.
c) Mark did better than about 68% of the students who took the test.
d) Mark did worse than about 68% of the students who took the test.
e) Mark got fewer than half of the questions correct on this test.

16. Check Your Understanding
Mark receives a score report detailing her performance on the statewide test. On the math section, Mark earned a raw score fo 39, which placed him at the 68th Percentile. That means that
c) Mark did better than about 68% of the students who took the test.

17. Check Your Understanding
2) Mrs. Munson is concerned about how her daughters height and weight compare with those of other girls of the same age. She uses an online calculator to determine that her daughter is at the 87th percentile for weight and 67th percentile for height.
Explain to Mrs.Munson what this means.

18. Check Your Understanding
3) About what percent of calls lasted less than 30 minutes? 30 minutes or more?
The graph displays the cumulative relative frequency of the lengths of phone calls made from the mathematics department office at Gabalot High last month.

19. Check Your Understanding
4) Estimate Q1, Q3, & the IQR of the distribution.

20. Standardized Scores (z-scores)
If x is an Observation from a distribution that has known mean and standard deviation, the standardized value of x is given by
Z = x- mean
Standard Deviation

21. Standardized Scores (z-scores)
If x is an Observation from a distribution that has known mean and standard deviation, the standardized value of x is given by
Z = x- mean
Standard Deviation
A standardized value is often called a z score.

22. Check for understanding Pg 91 #1-3
Lynette, a student in the class is 65 inches tall . Find and interpret her z- score.

23. Check for understanding Pg 91 #1-3
2) Another student in the class, Brent, is 74 inches tall. How tall is Brent compared with the rest of the class? Give appropriate numerical evidence to support your answer.

24. Check for understanding Pg 91 #1-3
3) Brent is a member of the school's basketball team. The mean height of the players on the team is 76 inches. Brent’s height translates to a z-score of -.85 in the team’s height distribution. What is the standard deviation of the team member’s heights?

25. TRANSFORMING DATA
-Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and spread of a distribution of data.

26. Effects of Adding or Subtracting a constant
Shape: The same
Center: Down or by the amount of the constant
Spread: The Same

27. Effects of multiplying or dividing by a constant (b)
Shape: The same
Center: multiplies (or divides) measures of center and location by b
Spread: multiplies( divides) the measures of spread by b

28. Check for understanding
Suppose that you convert a class’s heights from inches to centimeters (1 inch = 2.54 cm). Describe the effect this will have on the shape, center, and spread.

29. Check for understanding
2. If Mrs. N had the entire class stand on a 6 in. high platform and then the student measure the distance from the top of their heads to the ground, how would the shape, center, and spread of this distribution compare with the original height distribution? 

30. Check for understanding
3. Now suppose that you convert the class’s height to z- scores. What would be the shape, center, and spread of this distribution? Explain.  

32. Check for understanding